Final answer:
To find the acceleration of the system, we can use Newton's second law and calculate the gravitational force on each block. The total mass and the gravitational acceleration can be used to find the acceleration of the system.
Step-by-step explanation:
To find the acceleration of the system, we need to consider the forces acting on the two blocks. Since the surface is frictionless, the only force acting on the system is the gravitational force. We can calculate the gravitational force by multiplying the mass of each block by the acceleration due to gravity.
The acceleration of the system, a, can be calculated using Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration. Since the only force acting on the system is the gravitational force, we have F = m1g + m2g = (m1 + m2)a. Solving for a gives us a = (m1g + m2g) / (m1 + m2).
Plugging in the given values, m1 = 8 kg, m2 = 3.2 kg, and g = 9.8 m/s^2, we can calculate the acceleration of the system to be a = (8 kg * 9.8 m/s^2 + 3.2 kg * 9.8 m/s^2) / (8 kg + 3.2 kg) = 6.57 m/s^2.